Question

p is a point on the bisector of angle ABC. The line through P parallel to BA meets BV at Q. prove that triangle BPQ is an isosceles triangle​

Answer 1

Step-by-step explanation:

Given, P is a point on the bisector of angle ABC Also the line through P is parallel to AB and meets BC at Q.

To prove: BPQ is an isosceles triangle.

Proof: In the given figure, we have:

Angle ABP= Angle PBQ ( since BP is bisector)

Angle ABP= Angle BPQ ( Since AB parallel to PQ)

So, Angle PBQ= Angle BPQ

But they are the angles of Traingle BPQ.

Hence BPQ is an isosceles triangle.

(Proved)